This website uses cookies to deliver some of our products and services as well as for analytics and to provide you a more personalized experience. Click here to learn more. By continuing to use this site, you agree to our use of cookies. We’ve also updated our Privacy Notice. Click here to see what’s new.

About Optics & Photonics TopicsOSA Publishing developed the Optics and Photonics Topics to help organize its diverse content more accurately by topic area. This topic browser contains over 2400 terms and is organized in a three-level hierarchy. Read more.

Topics can be refined further in the search results. The Topic facet will reveal the high-level topics associated with the articles returned in the search results.

Abstract

The Young’s double-slit experiment is one of the most popular stories
in the history of physics. This paper, like many others, has emerged from the
Young’s idea. It investigates the diffraction of the plane or
spherical wave produced by three or four small holes in an opaque screen. It was
noticed that the interference field contained a lattice of optical vortices
which were equivalent to those produced in optical vortex interferometer. The
vortex lattice generated by the three holes possessed some unique properties
from which the analytical formulae for vortex points position were derived. We
also pointed out the differences between our case and the double-slit
experiment. Finally, some remarks on possible applications of our arrangement
are discussed briefly. These theoretical considerations are illustrated with the
use of experimental results.

Fig 3. The comparison between the experiment and the results of far field
computations. The circles correspond to the computed positions of the vortex
points. The crosses mark the vortex points localized in the interferogram.
Both figures differ in the arrangement of the three holes as shown under
each interferogram. The plates were inspected under microscopy while
applying to the calculations.

Fig. 4. The interference pattern obtained by adding the light emerging from the plate
with three holes together with an additional plane wave. The fork like
fringes indicates the presence of optical vortices. The vortex points
localized on this interferogram are marked with crosses.

Fig. 5 The position of vortex points calculated for the plate shown in Fig. 3(a) using far (pluses) and near (circles) field
diffractions integral (numerical integration). The positions of the three
vortex points were adjusted manually to show the difference between the
lattice determined by both methods.

Fig. 7. (a). The position of the vortex points for the plate shown in Fig. 3(a), calculated using parabolic (crosses) and
near (circles) field approximation, (b) comparison between computations
using parabolic field approximation and experimental results.

Fig. 8. The interference pattern produced by the four holes in the arrangement shown
below each interferogram. The vortex points (marked as crosses) were
localized by using minima method. Contrary to the three-holes case both
lattice shown in these interferograms are irregular.

Fig. 10. The spherical wave incident on the plate; here drawn in cross section. Since
the holes are small we can assume that each hole is illuminated by the plane
wave tangent to the given spherical wave at the hole center.

Fig. 11. When the plate is illuminated by the spherical waves the somb functions
representing the holes are mutually shifted in frequency domain. Here, for
simplicity somb function representing wave A and one of the other two waves
are plotted. For this reason in a given direction each hole contributes to a
different amplitude, which complicates remarkably the conditions for vortex
points positions.

Fig. 12 The vortex lattice shift due to small plate shift in the direction
perpendicular to the optical axis. Figure 12(a) shows two vortex lattices (circles-no
shift, x-after the test was shifted). Each lattice can be divided into two
sublattices which differ in the topological charge (the red signs plus and
minus are marked next to the vortices). The plus sublattices overlaps
– they have the same geometry. The minus sublattices are mutually
shifted. This is in agreement with our conclusions drawn from the theory. Figures 12(b) and 12(c) show the corresponding interferograms (before
and after the plate shift).

Fig. 13 The same experiment as in Fig. 13, but with four holes. This setup is much
more sensitive than the previous one, but the analysis is much more
complicated. The relevant methods are not ready yet.